Abstract

The low-energy spectrum of antiferromagnets reveal valuable information about the nature of the phase or phase transition in such systems. I review the recent works done in collaboration with Suwa and Sandvik [Phys. Rev. B 92, 195145 (2015), Phys. Rev. B 94, 144416 (2016)]on how to probe the dispersion of the excitations in a variety of SU(2) symmetric S=1/2 spin systems using quantum Monte-Carlo methods.Various applications are discussed in both one and twodimensions, which include probing the critical excitations for conventional and unconventional quantum critical points. Inthe latter case, the excitation spectrum is highly unusual and hasadditional gapless modes and possible emergent symmetries which are not present otherwise.